Which pathfinding algorithms can be applied on coloured graphs?
The idea is to apply a well known pathfinding algorithm (such as Dijkstra) on the graph given the rule: "only black and red edges"


Remove all the non-black-and-red edges from the graph first, then run it through any off-the-shelf pathfinding implementation.  Or implement your own, and have it completely ignore the non-black-and-red edges.